We study the parabolic Anderson problem, i.e., the heat equation ∂tu = ∆u + ξu on (0,∞) × Z d with independent identically distributed random potential {ξ(z) : z ∈ Z} and localised initial condition u(0, x) = 10(x). Our interest is in the long-term behaviour of the random total mass U(t) = Pz u(t, z) of the unique non-negative solution in the case that the distribution of ξ(0) is heavy tailed. ...

Despite their apparent simplicity, Web applications are surprisingly difficult to develop, if our aim is to build applications that behave correctly under regular conditions as well as adverse circumstances like out-of-order requests and race conditions. In this paper, we describe our experiences deriving customer-oriented acceptance tests for Web applications by modeling the essential capabili...

In this paper we consider bound state solutions, i.e., normalizable time-periodic solutions of the Dirac equation in the exterior region of an extreme Kerr black hole with mass M and angular momentum J . It is shown that for each azimuthal quantum number k and for particular values of J the Dirac equation has a bound state solution, and that the energy of this Dirac particle is uniquely determi...

Non-negative matrix factorization (NMF) is a widely used tool for exploratory data analysis in many disciplines. In this paper, we describe an approach to NMF based on random projections and give a geometric analysis of a prototypical algorithm. Our main result shows the proto-algorithm requires κ̄k log k optimizations to find all the extreme columns of the matrix, where k is the number of extre...

The paper presents a computational approach to reconstruct the shape of a perfectly conducting cylinder. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimum one. By using the genetic algorithm, the shape of the object can be reconstructed. The genetic algorithm will always conv...

In this paper we deal with the problem of studying some mathematical aspects regarding the polytope of fuzzy measures when the referential set is finite. More concretely, we study whether two extreme points are adjacent; for general polytopes, this is a NP-hard problem. However, for the case of fuzzy measures, we give a necessary and sufficient condition for two extreme points to be adjacent. T...

Non-extreme black hole solutions of four dimensional, N = 2 supergravity theories with Calabi-Yau prepotentials are presented, which generalize certain known doubleextreme and extreme solutions. The boost parameters characterizing the nonextreme solutions must satisfy certain constraints, which effectively limit the functional independence of the moduli scalars. A necessary condition for being ...